Form taken by potential energy

I have come across the following paragraph from my book"The gravitational force is always attractive .Whereas the electric force is attractive or repulsive acording to whether q0 is negative or positive.Each of the above forces is conservative,so a potential energy is associated with each of them.This potential energy must of course take the same form for both cases."
I want to know which form is it talking about?And why both cases would take the same form?

Staff: Mentor

I have come across the following paragraph from my book"The gravitational force is always attractive .Whereas the electric force is attractive or repulsive acording to whether q0 is negative or positive.Each of the above forces is conservative,so a potential energy is associated with each of them.This potential energy must of course take the same form for both cases."
I want to know which form is it talking about?And why both cases would take the same form?

By "form" they are saying that the equations look exactly the same, except perhaps for the letters that we use to represent the various quantities. For gravity we have Newton's ##F=Gm_1m_2/r^2## and for electrostatic force we have Coulomb's ##F=Cq_1q_2/r^2##. Look at these for a moment and you'll see that ##G## and mass are to the gravitational force equation as ##C## and charge are to the electric force equation; naturally the calculation of the potential energy works the same way for both.